SOLUTION: What is the greatest power of 3 that divides into 578!, with no remainder.

Question 1149796: What is the greatest power of 3 that divides into 578!, with no remainder.
Answer by ikleyn(52864) (Show Source): You can put this solution on YOUR website!
.


 = 192.66  gives you the factor  .


 = 64.22  gives you additional factor of  .


 = 21.41  gives you additional factor of  .


 = 7.43  gives you additional factor of  .


 = 2.37  gives you additional factor of  .


 = 0.79  will NOT give you additional factor of 3.


So, the maximal degree of 3 is   192 + 64 + 21 + 7 + 2 = 286.    ANSWER

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